In: Statistics and Probability
Suppose A consists of the people in the population who are asthmatic, and B consists of the people in the population who are allergic to cats. How would you describe the set (A∪B)∩(A¯∪B¯) in words?
(A U B) is the set of people who are either asthmatic or are allergic to cats
(
U
)
is the people that are either not asthmatic or are not allergic to
cats. That is, all people except those who are both asthmatic and
allergic to cats
(A U B)
(
U
)
consists of people belonging to both (A U B) and (
U
),
that is, the people who are either allergic to cat but are
not asthmatic or who are asthmatic but are not
allergic to cats.
(A U B)
(
U
)
is shown in Venn Diagram given below